Question: Simplify the following expression and state the condition under which the simplification is valid: $k = \dfrac{r^2 - r}{r^2 + r - 2}$
First factor the expressions in the numerator and denominator. $ \dfrac{r^2 - r}{r^2 + r - 2} = \dfrac{(r)(r - 1)}{(r + 2)(r - 1)} $ Notice that the term $(r - 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(r - 1)$ gives: $k = \dfrac{r}{r + 2}$ Since we divided by $(r - 1)$, $r \neq 1$. $k = \dfrac{r}{r + 2}; \space r \neq 1$